One of the suspected killers, identified as an Islamic State group sympathiser, was shot dead by police who said they were searching for at least one more assailant still at large.
However on Tuesday afternoon the Austrian government suggested there may only have been one shooter saying there was as yet no evidence of another gunman.
The attacks, in six locations including near a synagogue in the centre of the city, were carried out by “several suspects armed with rifles”, police said on Monday night.
The shooting began just hours before Austria was to re-impose a coronavirus lockdown, with people out in bars and restaurants enjoying a final night of relative freedom.
The death toll rose on Tuesday to four people, police said.
Vienna mayor Michael Ludwig earlier said that 15 people had been taken to hospital, seven of them seriously wounded.
Police said an officer had also been hurt during the attacks.
The attacks started at around 8 pm (1900 GMT) when the first gunshots were heard in the city's centrally located first district.
Interior Minister Karl Nehammer told a press conference Tuesday that the dead attacker was “a radicalised person who felt close to IS.”
“All the signs make it clear it's a radicalized person and a person who feels closely connected to IS.”
'An attack on Austrian values'
“We experienced an attack yesterday evening by at least one Islamist terrorist, a situation that we have not had to live through in Austria for decades,” Nehammer said.
“Austria for more than 75 years has been a strong democracy, a mature democracy, a country whose identity is marked by values and basic rights, with freedom of expression, rule of law, but also tolerance in human coexistence,” he said. “Yesterday’s attack is an attack on just these values.”
Police had used explosives to blast their way into the apartment of the dead man who had been “heavily armed”, the minister added
The editor of Vienna’s Falter newspaper said in Twitter messages that the assailant who was killed was known to domestic intelligence agencies, Reuters reported.
He had earlier noted that, “According to what we currently know, there is at least one attacker who is still on the run.”
It was unclear how many assailants were involved in the assault.
Speaking to ORF, Austrian leader Kurz said the attackers were “were very well equipped with automatic weapons” and had “prepared professionally”.
He had tweeted: “Our police will act decisively against the perpetrators of this repulsive terror attack.
“We will never be intimidated by terrorism and we will fight this attack with all means”.
Kurz said that while police were concentrating on the anti-terror operation, the army would take over the security of major buildings in Vienna.
Nehammer urged Vienna residents to remain in their homes and keep away from all public places or public transport. He said that children would not be expected to go to school on Tuesday.
Sirens and helicopters could be heard in the city centre as emergency services responded to the attack.
An AFP photographer said that large numbers of police were guarding an area near the city's world-famous opera house
The location of the initial shooting was close to a major synagogue.
The president of Vienna's Jewish community Oskar Deutsch said that shots had been fired “in the immediate vicinity” of the Stadttempel synagogue, but added that it was currently unknown whether the temple — closed at the time — had been the target of an attack.
Police in Vienna carry out stop and search checks in hunt for any more attackers. AFP
“It sounded like firecrackers, then we realised it was shots,” said one eyewitness quoted by ORF.
A shooter had “shot wildly with an automatic weapon” before police arrived and opened fire, the witness added.
At the busy bars and restaurants, people were told to remain indoors.
“At the beginning, I thought to myself that maybe we were making an American film or that they had drunk too much,” said waiter Jimmy Eroglu, 42.
But then he heard shots. “The police came in and said, 'you all have to stay inside because there's a probably a dead man there'”.
Robert Schneider, who lives in central Vienna, went out and found two lasers trained on his chest.
“Hands up, take off your jacket,” officers shouted at him, the 39-year-old told AFP. “We had seen nothing, heard nothing. We are in shock.”
Austria had until now been spared the sort of major attacks that have hit other European countries.
Police guard stand near Schwedenplatz square in the center of Vienna on November 3, 2020. AFP
President Emmanuel Macron of France, which has seen two serious attacks recently, tweeted that “we French share the shock and sorrow of the Austrian people”.
“After France, it's a friendly nation that has been attacked,” he added, referring to the killing on Thursday of four people by an attacker in the southern city of Nice after the beheading of a schoolteacher by a suspected Islamist outside Paris on October 16.
EU Council chief Charles Michel tweeted that the bloc “strongly condemns this cowardly act”, with European and global leaders also voicing support for Austria.
Czech police said they were conducting random checks on the border with Austria.